We have next addressed the coalescence of droplets in the case of two parallel vortices, one in each droplet, perpendicular to the merging direction and
with opposite quantum circulation (vortex dipole, see Fig. REF ), which has a total angular momentum \(\langle L \rangle = 0\) .
Since the phase difference between the superfluid
droplets at the touching point is \(\pi \) , a dark soliton is expected to appear at the contact region.
We recall that a dark soliton is a structure (a disk in the present case) made
of nodal points of the effective wave function \(\Psi (\mathbf {r},t)\)  were the real and imaginary parts are both zero;[1]}
this is at variance with vortices, where the nodal points form a line.
